906 A. B. BLAKEAND F. A. COTTON
Inorganic Chemistry CONTRIBUTIOX FROM THE DEPARTMENT O F CHEMISTRY, INSTITUTE OF TECHNOLOGY, CAMBRIDGE 39, MASSACHUSETTS MASSACHUSETTS
Calculation of Pseudo-Lattice Energies and the Estimation of Metal-Ligand Bond Energies in Some Tetrahedral Tetrachlorometallate(I1) CornplexedtL BY A. B. BLAKE
AND
F. A. COTTOK1b
Received illarch 23, 1963 A method of calculating the pseudo-lattice energy, that is, the energy required to separate a crystalline compound containing complex ions into gaseous species so that the complex ions remain intact, is described in detail. The feasibility of the method depends on the availability of an efficient program for machine computation of Madelung energies; such a program is described. I t is shown how the pseudo-lattice energy may be used together with experimentally accessible thermodynamic data t o calculate the complexation or ligation energy, ie., the energy released when a gaseous complex ion iq formed from a gaseous metal ion and gaseous ligands. The entire procedure is illustrated for the complex ions [CoClr]2-, [ C U C I ~ ] ~and - , [ZnClr12-, and in the case of [CoCL]2 - a valuable check is provided by the acceptable agreement between the results obtained using CSZCOCL and CsaCoCls. The significance of the energies of complexation in relation t o problems of ligand field stabilization and bond character are briefly discussed.
Introduction
It has been shown2 that enthalpies of complexation or ligation, that is, the enthalpies, AH,,,, of reactions of the type [MLzlnfc"(g) = Mn(g) 4-ZL"(g)
AHoom
(1)
could be evaluated by setting up a thermodynamic cycle which involves a term called the pseudo-lattice energy. The latter is the energy required to separate a crystalline compound containing complex ions into gaseous species in which all complex ions remain intact in the gas. Results were presented for a series of reactions of the type [M("a)6]2+(g)
= M"(g)
+ 63"3(g)
as well as some other similar ones. It should be noted that this method appears to be the only one capable of providing the fundamentally important complexation energies, AH,,,, themselves, rather than some quantity which is the sum of AH,,, and one or more others which cannot themselves be easily measured or calculated. For example, i t is fairly easy in a great many cases to determine from readily accessible experimental data the enthalpy of dissolving gaseous cations and anions into an aqueous solution of a ligand. From this datum, however, one can obtain only a quantity which is the sum of AH,,,, the hydration energy of the gaseous complex ion and the hydration energy of the counter-ion. Since there is no certain method of separately measuring or calculating the two hydration energies, or their sum, AH,,, alone cannot be extracted from the experimental datum. I n their excellent survey of the thermodynamic consequences of inner-orbital splittings, George and McClure3pointed out that despite the advantage of having AH,,, values, the above method for obtaining them was limited in applicability b y (1) a lack of data on the heats of formation of the crystalline complex compounds and (1) (a) Supported by the United States Atomic Energy Commission. (b) Fellow of the Alfred P.Sloan Foundation. (2) F. A. Cotton, Acfa Chem. S c a d . , 10, 1520 (1956). (3) P. George and D. S. McClure, Puogv. Inorg Chem., 1, 381 (1959).
(2) the difficulty of calculating the pseudo-lattice energies for structures more complicated than the cubic ones considered in ref. 2. The first of these limitations is relatively unimportant, since quite straightforward calorimetric measurements of only moderate accuracy will provide the necesary heats of formation, as illustrated, for example, by the measurements reported here, and more extensive ones to be reported in another paper from this laboratory.4 A major purpose of this paper is to show how, with the availability of fast digital computers, the second limitation also becomes inconsequential. This is because programs can be written for rapid computation of Madelung energies of any arbitrary array of ions, however little symmetry i t may have. In this paper we shall treat the general theory of computing pseudo-lattice energies and illustrate the method in the cases of Cs2CoC14, Cs~CuCL,and Cs2ZnC!14, which have structures for which no Madelung constant can be written analytically. The enthalpies of the processes [MCIrI2-(g) = M2+(g)
+ 4Cl-(g)
(2)
will be reported and discussed. The digital computer program used for computation of the Madelung energies will also be described (see the Appendix). Procedure The thermodynamic cycle to be utilized is 2CsYg)
+ M2*(g) + 4C1-(g) +- 2Cs+(g) + [MCC12-(g)
AHr[Mz"(g)l 2AHr[Csf(g)l 4AHf[Cl-(g)]
AHmm
1
T
AHL
I
I
elements in std. states
AHi [CszMCla(s)]
----+CSZMCMS)
This provides the thermochemical equation AH,,,
+ A H L = AHi[M2'(g)1 + 2AHi[Cs"(g)] +
4AHi[CI-(g)] - AHi[Cs,MCla(s)]
(3)
(4) A. B. Blake and F. A. Cotton, Inoug. Chem., submitted for publication.
CALCULATION OF PSEUDO-LATTICE ENERGIES907
Vol. 2, No. 5 , October, 1963 The values of the first three terms on the right side of eq. 3 may be found in the literature. AHt[M2+(g)] values are given in Table IXA of ref. 3 and the other two quantities are given in the NBS tables6 The heats of formation of the three CsBMCll compounds were determined by the method of ref. 4; pertinent details are given in the Experimental section and in Table IV. The pseudo-lattice energies were calculated in the manner described in the following section. Table I records
TABLE I THERMODYNAMIC DATAFOR EQUATION 3, IN AHr[M2+(g)l 2AHr [ Cs+( g)] 4AHr[Cl-(g)] - AHf[CszMClr(s)] AHoom AHL AHL
+
AHmm
KCAL. /MOLE
co
cu
Zn
681.2 220.2 -241.2 294.7 954.9 329 f 2 625f2
732.3 220.2 -241.2 263.5 974.8 333 f 2 642 f 2
664.7 220.2 -241.2 323.5 967.2 329 f 2 638f2
u, a scale factor by whicb we can measure the expansion or contraction of the crystal in such a way that all the interatomic distances ( p and T) change by the same fraction as the scale factor changes. Thus, all distances remain in fixed ratios, but their magnitudes are given by the expressions (6)
pzj = upOz1 711
=
UT011
UM’is a partial lattice sum extending only over pairs of atoms both lying within one complex ion. Disregarding the proportionality constant required before each summation to put results in kcal./mole, we may then write UMT =
cc
i>l
3
+
;;;l
c c,;::“u
k>Z
1
whence the values of all the quantities occurring in eq. 3 for each of the three systems under consideration. Computation of Pseudo-Lattice Energies.-We assume that A H L can be estimated with the necessary accuracy by considering only those contributionsa -AHL
=
UM
+ Un + UR 4- Uz
(4)
specified in eq. 4, in which all quantities are a t O’K. Correction of AHLto the room-temperature value will be discussed later. UMis the Madelung energy, i e . , the sum of all pairwise coulombic interaction energies. UD represents the total attraction energy due to dispersion forces (van der Waals or London energy). UR is the repulsion energy. UZ is the zero-point vibrational energy. It should now be emphasized that from the definition of AHL, the first three terms on the righthand side of eq. 4 refer exclusively to interactions between atoms which do not lie within the same complex ion. Evaluation of Uhr.-We define U M in the following way UM =
UMT(PO,TO,p,U)
-
uM1(To&l~U)
Using the computer program described in the Appendix, MT,MI, and hence M can be calculated with little effort for any crystal of known structure ( i e . , known atom coordinates) and foi any desired values of the fractional charges on the atoms. treatment here parallels Evaluation of &.--The that used for the Madelung energy. Thus we write UD
UDT(pO,TO,U) - uD1(To,U)
(8)
where we make the approximation of neglecting any dependence of dispersion energy on the distribution of fractional charges over the atoms in the complex ion. Now, explicitly, we have for the UDterm
and
(5)
U N is~the complete lattice sum taken over all atoms in the crystal. It is a function of the following four parameters : q, representing the net (integral or fractional) charges on the atoms. In the present case we take qcS to be fixed a t +1, but q c ~and qc0 may vary subject only to the limitation 4qc1 qc0 = - 2 . T O , representing the set of equilibrium interatomic distances between all pairs of atoms within one complex ion as i t exists in the crystal, pot representing the set of equilibrium interatomic distances between all pairs of atoms not both lying within one complex ion.
where the Cijare of six types only, viz., Ccscy,CC~CI, Cclcl, C h f ~CMCI, , and C M C ~For . computational purposes it therefore proved simplest to regroup the terms in the sums constituting U D into ~ Six separate sums of the type
+
( 5 ) “Selected Values of Chemical Thermodynamic Properties,” U S. Department of Commerce, National Bureau of Standards, Circular 500, Washington, D. C , 1961. (6) A good background for the present discussion will be found in F. Seitz, “The Modern Theory of Solids,” McGraw-Hill Book Co., New York, N. Y.,1940, Chapter 2.
A Fortran computer program was then written to calculate sums over r+, the input being the atom positions in the unit cell. The series were terminated upon reaching a term which was less than a certain predetermined fraction of the sum.’ The sums over (roiJ)-6 ?(7) The correctness and accuracy of this program were checked by using i t t o compute van der Waals energies for NaCl and CsC1. The results agreed satisfactorily with those previously obtained using analytical expressions by Jones and Ingham.8 (8) J. E. Jones and A. E. Ingham, PYOC. Roy. SOG.(London), AlOT, 636
(1925).
908 A. B. BLAKEAND F. A. COTTON appearing in the UD' term are of course few and easily evaluated by hand. These were subtracted from the The CABvalues were complete lattice sum over r 6 . chosen in the following way. Three of them were taken from the literatureg CcBcs= Cclci
=
Inovganic Chemistry from that a t 0°K. it is necessary to add to it the quantity
loo
C,[MCL-( g)]dT
129 X 10-60 erg-cm.6
CcScl = 152 X
erg-cm6
None of the three CABvalues involving the metals hf could be found in the literature. Assuming them all erg-cm6,the total contribution of the to be 140 X terms involving them is only 4 kcal./mole. The above estimate is not likely to be in error by more than i.50 X 10-6O erg-cm.6,thus introducing an error of less than 0.5 kcal./mole into the final result because of the form of eq. 15. It was not, therefore, considered worthwhile to attempt any more refined estimates of C M ~CMCI, I , and
ems.
Evaluation of UR.-We have elected to use an expression of the Born type rather than the more rigorous Born-Mayer exponential type. This is justified in view of the relatively low level of accuracy (=I=-3 kcal./mole) to which we are restricted by other approximations and uncertainties. Thus we write
The summation is over only those interatomic distances which are not internal to one complex ion. In order t o eliminate B , we follow the well known procedure of differentiating the expression for the pseudo-lattice energy, viz.
The value of the first integral was roughly estimated as 7 f 1 kcal.,'mole. The entropy of Cs2MC14(s) a t 300'K. was estimated to be 50 10 e.u., exclusive of that due to internal vibrations of the MC1d2- ion, and a set of Debye functions was selected to fit this entropy; from these functions the integral was evaluated. The second and third terms were estimated by standard statistical mechanical methods (treating the complex ion as vibrationless, however), giving for their sum 6 =t 0.5 kcal./mole. Thus the net correction to -AHL is -1 kcal. 'mole.
*
Results The results of the computations for CsnCoClr, Cs2CuC14, and CszZnC14are summarized in Table 11. In each case the calculation of M has been made for eight different charge distributions in the complex ion. The results for Cs&!uCl, are plotted in Fig. 1. I t can be
0,
350
E \ -
0
Y" with respect to internuclear distances as measured by the scale factor, u,and equating the result to zero as the condition of equilibrium, thus obtaining
Solving this equation for B in terms of M and C and inserting the result in eq. 13 we obtain the final equation for computation of the pseudo-lattice energy
340
.-C _I
I
a
330
I t2
0
-2
Charge on Copper Fig. 1.-The variation of the pseudo-lattice energy of Cs2CuCIi ~with charge distribution in the [ C U C I ~ ]ion.
Since the repulsive energy being considered arises from interactions among cesium ions and chlorine ions only, it is correct to assign to n, the repulsion exponent, a value of 10, i.e., that which has been shown6to be appropriate for CsC1. UZand Correction to 300°K.-Estimating the Debye maximum frequency, vmaxr to be 100-200 cm.-l, and using the relation U Z = (g/4)nNh~,,x, in which N is Avogadro's number, h is the Planck constant, and n, the number of atoms per formula unit, is taken as 3 for Cs2[MC14],we obtain 0.5 < U Z < 1.0 kcal./mole. We have therefore taken 1 kcal./mole as the value of UZ in all of the Cs2NIC14 compounds. In order to obtain the value of - A H L a t 300'K. (9) J. E. Mayer, J Chein Phys , 1, 270, 327 (1933)
seen that the dependence of AHI,upon charge distribution is linear within the significance of the numbers and also that the total range of variation is fairly large, viz., -,30 kcal.,'mole. For use in calculation of AH,,, we have selected values of AHL. corresponding to a charge on the metal of 0.5 f 0.25. This choice is, of course, to some extent arbitrary, but seems in reasonable accord with inferences which may be drawn from various lines of experimentallosll evidence and theoreticall*!l 3 considerations. (10) K . Kubo, et a l . , J . A m . Chenz. SOL.,8.3, 4526 (1961). (11) C. K. JZrgensen, Progr. Inovg. Chem., 4, 73 (1962). (12) C. J. Ballhausen, "Introduction t o Ligand Field Theory," McGrawHill Book Co., 4 e w York, N. Y . , 1962, p. 163. (13) L. Pauling, "The Nature of t h e Chemical Bond," 3rd E d . , Cornell University Press, Tthaca, N. Y., 1960, p 172.
CALCULATION OF PSEUDO-LATTICE ENERGIES909
Vol. 2 , No. 5, October, 1963
TABLE I1 CALCULATED PSEUDO-LATTICE ENERGIES OF Cs2CuClpAND Csd2oCla FOR VARIOUS CHARGE DISTRIBUTIONS IN THE ANIONS -M,& - C,Q - uz, Heat capacity Charges on-
7 -
M
M
c1
;:[1;E#;
kcal./ mole
kcal./ mole
kcal./ mole
AHL a t 300°, kcal./mole
corr., kcal./mole
-1.0 326.1 31.3 -1.0 -1 348.4 -1.0 328,8 31.3 -1.0 -0.9 351.5 -1.0 331.7 31.3 -1.0 -0.8 354.7 -1.0 334.8 31.3 -1.0 -0.7 358.1 -1.0 338.0 31.3 -1.0 -0.6 361.7 cu -1.0 341.4 31.3 -1.0 -0.5 365.5 -1.2 -0.2 378.0 31.3 -1.0 -1.0 352.7 -1.0 357.7 383.6 31.3 -1.0 0 -1.0 317.2 -1.0 342.5 27.5 -1.0 -0.9 346.0 27.5 -1.0 -1.0 321.4 -1.0 323.5 -0.8 349.5 27.5 -1.0 27.5 -1.0 -1.0 326.9 -0.7 353.2 co 330.2 27.5 -1.0 -1.0 -0.6 356.9 -1.0 333.5 360.6 27.5 -1.0 -0.5 344.2 -1.2 -0.2 372.4 27.5 -1.0 -1.0 -2.0 0.0 378.3 27.5 -1.0 -1.0 349.5 Crystal structure data taken from the following sources: CszCoCl4, M. A. Porai-Koshits, KktuZZogmjiu, 1, 291 (1956); Cs2ZnC14, B. Brehler, 2. Krist., 109, 68 (1957), reported t o be isomorphous with the Co compound-X-Ray powder pictures of the two comCs2CuC14, B. Morosin and pounds, taken in this laboratory, are indistinguishable and unit cell dimensions differ by less than 0.005 E. C. Lingafelter, J . Phys. Ckem., 65, 50 (1961).
:i;
Fi!
Q
a.;
In the case of the [CoC14I2- ion i t has been possible to make a severe test of the validity of the procedure and of the numerical correctness of the result. This is because the [c0C14]~-ion also occurs in another suitable compound with a different but known structure, namely, csQcoc16, which consists of 3cs+, and [CoC14I2- ions.14 For cs&oc16 the results of the lattice energy calculation are collected in Table 111. Now i t is easily shown that the value of AH,,, AHI, obtained from Cs&o!C16 should be equal to that obtained from Cs&oCI( augmented by the quantity
el-,
+
AHt[Cs+(g)]
+ AHf[Cl-(g)l
-b
AHf[CsaCoCL(s)] - AHf[C~aCoCli(s)]
We have measured the heat of formation of Cs&oC&(s) and obtained a value of 399.2 kcal./mole. Using this value, together with others from Table I, we obtain for AH,,,, AHLfor Cs&oC& a value of 1110.2 kcal./ mole. From Table I11 we interpolate a value of A H L for a charge of + l / 2 on cobalt of 503 f 10 kcal./mole. Thus, the value for AH,,, obtained from c s s c o c ~ 6is 607 f 10 kcal./mole, which is to be compared with the value of 625 f. 2 obtained from Cs2CoC14. The discrepancy of 18 f 12 kcal./mole, where the limits quoted are based only on the range of uncertainty in selection of the charge distribution, is perhaps larger than would be expected. Several factors may be considered in explanation. First, although we have proposed a charge distribution in the [MC14l2- complexes which places a charge of +0.5 i 0.25 on M, it must be admitted that this is scarcely more than an educated guess; it is not impossible that it is a very
+
(14) The structure was originally reported by H. M. Powell and A. F. Wells, J Chem. S o c , 359 (1935). Recently, however, i t has been reexamined by Dr. R. Mason of Imperial College, London (private communication, t o be published), who obtains somewhat different and much more reliable atomic coordinates. Mason's results were used in this work.
TABLE I11 CALCULATED PSEUDO-LATTICE ENERGY OF CssCoClsFOR VARIOUS IN [CoC14]2CHARGEDISTRIBUTIONS -M,
-C,
-Uz,
Charges on co c1
kca1.l mole
kcal./ mole
kcal./ mole
Heat capacity corr., kcal./ mole
1.6 1.2 0.8 0.4 0.0
606.3 578.3 555.6 538.2 526.1
41.7 41.7 41.7 41.7 41.7
-1.0 -1.0 -1.0 -1.0 -1.0
-1.0 -1.0 -1.0 -1.0 -1.0
-0.9 -0.8 -0.7 -0.6 -0.5
AH5 at 300'. kcal.1 mole
560.4 535.2 514.7 499.1 488.2
poor one. If, for example, a charge of zero is assigned to cobalt, the discrepancy is only 7 kcal./mole, which is certainly acceptable. Quite generally, the selection of the correct charge distribution within polyatomic ions constitutes the most vexing difficulty in the entire pseudo-lattice energy treatment, because there is no straightforward way to estimate charge distribution from any experimental data (so far as we know) and theoretical estimates based on, say, molecular orbital calculations would be tedious in any event and of quite uncertain reliability. Fortunately, in many cases, e.g. , the Cs2MC14 salts treated here, the results are not extremely sensitive to the charge distribution over a very broad range (for qcUfrom 0.0 to 1.0 the spread is only 8 kcal./mole). I t is also possible, however, that a t least part of the discrepancy in the results obtained for c0c142- is real. In cs&oc16 the coC14-2 ion is considerably more and differently distorted (Dad symmetry, all Co-cl equal, angles 106' (2) and 111' (4)) than in Cs~Coc14. A separate pseudo-lattice energy calculation for CSZZnC14 was not required because the positional parameters of the atoms in this compound are evidently almost identical with those of corresponding atoms in CszCoClr (see footnote to Table 11).
+
910 A. B. BLAKEAKD F. A. COTTON Discussion The major emphasis in this paper is on examination of the premises and derivation of general equations for the computation of pseudo-lattice energies and on the presentation of a satisfactory procedure for the actual performance of ‘such computations. There have, in the past, been several attempts to compute Madelung energies of substances containing polyatomic ions but because of computational limitations they have usually assumed the charge on a complex anion (or cation) to be entirely localized on the central atom2,15 or, alternatively] used only the extreme ionic distribution of chargelfi(e.g., treated NOS- as N6f and 302-). I n one simple case, namely, that of linear, symmetrical triatomic ions (e.g., Na-, FZH-), expressions have been derived for a charge distribution c ~ r r e c t i o n . ~However ~ , analytical treatments of this kind are not in general practicable for more complicated polyatomic ions, and a method such as ours, based upon machine computation of the total lattice sum for a variety of preselected charge distributions, seems to be the best general solution to the problem. In the present paper, we report results only for systems in which the atoms were selected to allow relatively unambiguous choices, based on precedents, for the repulsion exponent and the factors C occurring in the dispersion energy expressions. It should be pointed out that there are many complex ions of interest which crystallize only with polyatomic counter-ions. In such cases criteria for selection of the above-mentioned parameters will have to be developed. However, because of the low sensitivity of the pseudo-lattice energies to the magnitudes of n and C in eq. 15 this should not prove to be an insuperable difficulty in more general application of the sort of treatment reported here, provided results of only moderate precision (say =+=lo kcal./mole) are desired. With regard to the specific results obtained for the [MCl4I2-ions, a few comments may be made. First of all, it may be noted that, although ligand field stabilization energies may play some role in making tetrahedral complexes of some ions more stable than those of other^,^ their importance in the over-all energy of complexation is slight. Thus for the [MC14I2- ions in the series with M = Fe, Co, Nil and Cu, these stabilization energies are -10 kcal./mole4 and are thus only -1.5% of the entire AH,,,. Although there is now a great deal of experimental data to show that the bonds in complexes in generalI8 and in [CoX4I2- species in particularlg have considerable covalent character, this is not evident iron en(15) A. P. Altshuler, J. Chem. Phys., 23, 1561 (1953). (16) Far a detailed and authoritative discussion of thesc older calculations (and much other general information on lattice energy calculations), see T. C. Waddington, Adua7z. Iizorg. Chem. Radiochenz., 1, 157 (1959). (17) P. Gray and T. C. Waddington, Pvoc. Roy. Soc. (London), A235, 481 (1956). We have used our method t o recalculate their results for KN-3, as a check on both methods. The results agree within 1 kcal./mole. (18) F. A, Cotton and G. Wilkinson, “Advanced Inorganic Chemistry, A Comprehensive Course,” Interscience Publishers, New York, N. Y . , 1962, p p . 590-596. (19) F. A. Cotton, D. hI. L. Goodgame, and M. Goodgame, J . A m . Chem. Soc., 83, 4690 (1961).
IBorgunic Chemistry ergetic considerations alone. Thus the magnitude of AH,,, calculated by treating [CoC14Ia- as an array of four charges, -e, tetrahedrally arranged about a charge +2e, with the distance between opposite charges equal to the mean observed Co-C1 distance in Cs2CoCl4,is 652.3 kcal./mole. If one further assumes that for real e o z +and (21- ions a repulsive energy of 5 1 0 % of the total attractive energy should also be consideredz0we estimate AH,,, to be 587-622 kcal./mole for purely “ionic” metal-ligand bonds, whereas the value of AH,,, estimated from experimental data is -616 kcal./mole. We thus conclude that energetic considerations alone cannot be used as a criterion of bond type. This may actually have some advantage in that rough estimates of bond energies may be obtainable by assuming pure ionic bonds even though this is unrealistic. Naturally, i t cannot be asserted that this is generally so on the basis only of the one example discussed.
Experimental Apparatus.-The heats of solution were measured with the twin-chamber calorimeter t o be d e ~ c r i b e d . ~The heat absorbed or evolved was balanced by a directly measured quantity of electrical energy supplied t o a heating coil in either the solution or reference chamber, t o nullify the temperature difference produced by the solute. All experiments were a t an initial temperature of 25 & 0.1 ’. Materials.-CsC1 of 99.9% purity was obtained from Fairmount Chemical Company. CoC12.6Hz0, ZnClz, ZnS04.7Hz0, KC1, and KzS04 were Mallinckrodt A.R. grade. The zinc sulfate was kept in a desiccator over water saturated with KNOa and NHaCl. CszCoCl4 was prepared by slow evaporation of an aqueous solution of cesium chloride and cobalt chloride ( 2 : l ) and analyzed electrolytically for Co. Anal. Calcd.: Co, 12.63. Found: Co, 12.80. CszZnC14was prepared by mixing solutions of cesium chloride (1 M ) and zinc chloride (0.5 M ) in hot 6 AI aqueous HCI and cooling the solution. CszCuCll was prepared by dissolving 6 g. of CuClp.2HzO and 25 g. of CsCl in 50 ml. of hot water, filtering the solution, and evaporating it t o 25 ml. on a steam bath, with occasional stirring. After cooling, the golden yellow needles were filtered and dried for 1 hr. a t 130”. CSCOCISwas obtained by evaporating a solution made from 6 g. of CoClz.BHz0, 26 g. of CsC1, and 50 ml. of watcr t o 25 ml., allowing it t o stand about 4 hr., and then filtering off the crystals and drying them several hours a t 130”. Results and Treatment of Data.-The entire approdcli is analogous to that outlined in rcf. 4. Experimental data collected were for the reactions
+ KzS04(s) + 1000H20(1)= solution ( AHs* for Zn) 2CsCl(s) + ZnS04.7H20(s)+ 2KCl(s) + CszZnC14(s)
993HzO(1) = solution (
+ 1000H?0(1) solution + CuC1?.2HpO(l) + 998HJ0(1) =
Cs2CuC14(s) 2CsCl(s)
=
for Z n )
( l I I a kfor Cu)
solution ( AHBBfor Cu)
(20) In this connection, it is pertinent t o comment on Ballhausen’s contention21 t h a t a n electrostatic picture of metal-ligand bonding can be ruled out a priovi because “we know from Earnshaw’s theorem of electrostatics that no system of charges can be in stable equilibrium while a t rest.” This is true in a limited sense, b u t is not relsvant t o a model in which w e assume that the forces of attraction between the metal ion and the ligands (as well as part of the repulsive force between ligands of like charge) are purely electrostatic, but in which we also introduce noncoulombic repulsive forces of unspecified origin, This is a model quite analogous t o the one commonly used t o treat “ionic” solids such as SaC1. We believe the relevant question is whether this model, which does i t o l violate Earnshaw’s theorem, is tenable as far as energetics are concerned, and it is t o this question t h a t our discussion here is addressed. (21) Reference 12, p. 152.
STATIC DISTORTIONS OF TRANSIPION METALCOMPLEXES911
Vol. 2 , No. 5, October, 1963 CszCoCl4(s) 2CSCl(s)
+ lOOOHzO(1)
=
solution
(AH,A for Co(1))
TABLE IV MEASURED ENTHALPIES= OF THE SOLUTION PROCESSES~ Metal AH,^, AH,^,
+ CoC12.6HzO(s) + 994Hz0(1) =
solution ( AHs* for Co( 1))
Cs&oCls(s) 3CsCl(s)
+ 1000H~0(1)= solution
(AHsA for Co(2))
+ CoClz.BHzO(s) + 994Hz0(1) =
solution (AH,= for Co(2))
The results are recorded in Table IV. When used together with other data obtained from ref. 5, these data permit us to calculate the standard enthalpies of formation of the CszMC14 compounds and CsaCoClS.
Appendix Machine Computation of Madelung Energies A Fortran-coded program has been writtenz2 for calculating the electrostatic (Madelung) part of the cohesive energy of an ionic crystal on the IBM 709/7090 computer system. The program is based upon the method of E ~ a l dand ~ ~utilizes Bertaut’s device24of representing the ions as symmetric gaussian charge distributions of variable distention. Provision is also (22) The valuable assistance and advice of Mr. J. P. Wright are acknowledged. (23) P. P. Ewald, A n n . Physik, 64, 253 (1921). (24) E. F. Bertaut, J . phys. uadium, 13, 499 (1952).
ion
kcal./mole
kcal./mole
Zn 13.8 3.8 cu CO(1) -0.3 CO(2) 4.8 0 All values are the averages of the results of concordant measurements. Mean deviations are 10.05 kcal./mole. See Experimental section equations of the processes.
*
20.0
3.7 11.1 15.1 two or more all less than fo:- chemical
made for checking the degree of convergence of the series in the manner suggested by Templeton.25 The inpout data required are the unit cell parameters (edges in A. to four decimal places and cosines of angles to four decimal places) , the fractional coordinates (to four decimal places) of all atoms of a given kind in the unit cell, and the charges (to two decimal places) of each kind of atom. The machine time required on the 7090 to compute each of the M values used in this work was -1.2 min. An outline of the theory, directions for using the program, and a Fortran deck may be obtained by addressing requests to F. A. C. (25) D. Templeton, J . Chem. Phys.,
as,
1629 (1955).
CONTRIBUTION FROM THE DEPARTMENT O F CHEMISTRY HARVARD UNIVERSITY, CAMBRIDGE 38, MASSACHUSETTS
A n LCAO-MO Study of Static Distortions of Transition Metal Complexes BY L. L. LOHR, JR.,
AND
WILLIAM N. LIPSCOMB
Received April 16, 1963 The one-electron-LCAO method in which all valence orbitals are included has provided a semiquantitative basis for “JahnTeller” distortions in VCl4, C U C ~ ~NiClaT2, -~, CuFa-‘, and for the spectra of these ions.
Introduction The dynamic,’ i.e., vibronic, Jahn-Teller2 effect in transition metal complexes has received recent attention, but little even semiquantitative basis has been provided for the supposedly simpler static effect.a,4 The problem is one of molecular conformation, for which the recent application of a molecular-orbital (MO) one-electron LCAO method has shown some success.5 All valence orbitals are used in this method, (1) w. Moffitt and w. Thorson, Phys. Rev., 108,1251 (1957): A. D. Liehr, J . Phys. Chem., 64, 43 (1960); A. D. Liehr, A n n . Rev. Phys. Chem., 19, 41 (1962); A. D. Liehr, J . Phys. Chem., 67, 389, 471 (1963). (2) H. A. Jahn and E. Teller, PYOC.Roy. SOG.(Idondon),8161, 220 (1937); H. A. Jahn, ibid., A164, 117 (1938). (3) “It is a great merit of the Jahn-Teller effect that it disappears when not needed,” J. H. Van Vleck, J. Chem. Phys., 7 , 61 (1939). (4) U. 6 p i k and H. M. L. Pryce, Puoc. Roy. SOC.(London), 8238, 425 (lQ57); L. E. Orgel and J. D. Dunitz, Natuve, 179, 462 (1957). ( 5 ) I,. L. I.ohr,-Jr., and W. N. Lipscomb, J. Chem. Phys., 88, 1607 (1963); T. Jordan, H. W. Smith, L. L. Lohr, Jr., and W. N. Lipscomb, J . A m . Chem. Soc., 8 5 , 846 (1963).
but nuclear repulsions are ignored because they are simulated6 by over-estimated antibonding electronic interactions.6 Also explicit and detailed electronelectron repulsion terms are included only in an average way. Therefore, the results described here are mostly confined to V(1V) and Cu(I1) systems in which one electron or one hole occurs, respectively, and hence the one-electron approximation also describes the complete electronic states of complexes of these ions rather well. Some extension is made to Ni(I1) and Co(I1) high-win svstems. containing ” two and three unDaired electrons, respectively. In particular, the vc14 molecule and the CUC~A-’. NiCld-z. and C U F R -ions ~ are - , - , treated here as Of this ‘lass Of species in which a semiquantitative basis is desirable for the magnitudes of static Jahn-Teller distortions. “
I
. I
(6) J. C . Slater, “Quantum Theory of Molecules and Solids,” Vol. I , McGraw-Hill Book Co., New York, N. Y., 1963, p. 106.
